Multiply and Divide Like a Pro

🚀 Imagine you run a business packing 1,248 chocolate bars into boxes of 6. How many full boxes do you get? Any left over? Or picture printing 2,345 festival programmes and needing 14 times that many leaflets. These are real problems that real people solve every single day using two powerful tools: long multiplication and short division. By the end of this lesson you will be able to tackle both with confidence and — crucially — decide what to do with any awkward remainders that pop up.

Long multiplication is a written method for multiplying a large number by a two-digit number. The key idea is to split the two-digit multiplier into its tens and ones, multiply separately, then add the two results together. This works because of the distributive law: 1,248 × 14 is the same as (1,248 × 10) + (1,248 × 4). We write the partial products — the two separate multiplication answers — one under the other before adding. The zero placeholder in the second row is essential: it shows we are multiplying by tens, not ones.

Here is how to set out 1,248 × 14 step by step. Write 1,248 on top and 14 below, aligning digits in columns (thousands, hundreds, tens, ones). Step 1: multiply 1,248 × 4 (the ones digit). 4 × 8 = 32, write 2 carry 3. 4 × 4 = 16, plus 3 = 19, write 9 carry 1. 4 × 2 = 8, plus 1 = 9. 4 × 1 = 4. First partial product: 4,992. Step 2: multiply 1,248 × 10 (the tens digit). Write a 0 in the ones column as a placeholder, then multiply 1,248 × 1. Second partial product: 12,480. Step 3: add — 4,992 + 12,480 = 17,472. ✅

Short division is the compact written method for dividing a large number by a single digit. You work through the digits from left to right, one column at a time. Any amount that does not divide exactly is carried to the next digit — this is called carrying the remainder. For example: 1,248 ÷ 6. 6 into 1 = 0 remainder 1, carry the 1. 6 into 12 = 2 remainder 0. 6 into 4 = 0 remainder 4, carry the 4. 6 into 48 = 8. Answer: 208. The method keeps everything neat and avoids the long subtraction steps used in long division.

Sometimes a division does not come out exactly and you end up with a final remainder. What you do with it depends entirely on the context — the situation the problem describes. There are three choices: 1️⃣ Leave it as a whole-number remainder (e.g. 19 ÷ 4 = 4 r 3). 2️⃣ Express it as a fraction — put the remainder over the divisor (e.g. 19 ÷ 4 = 4 and three-quarters, written 4¾). 3️⃣ Round the answer up or down to the nearest whole number depending on what makes sense.

Great work! Let's pull it all together. Long multiplication splits a two-digit multiplier into tens and ones, creates two partial products, uses a zero placeholder for the tens row, and finishes with an addition. Short division works column by column from left to right, carrying remainders as it goes. A leftover remainder at the end must be interpreted using the context: leave it, write it as a fraction, round down, or round up. Mastering these three decisions is what separates a calculator user from a real mathematical thinker. 🧠 Now try the quiz!